Answer:
see explanation
Step-by-step explanation:
the equation of parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier.
here (h, k ) = (3, 1 ) , then
y = a(x - 3)² + 1
to find a substitute any other point on the graph into the equation.
using (0, 7 )
7 = a(0 - 3)² + 1 ( subtract 1 from both sides )
6 = a(- 3)² = 9a ( divide both sides by 9 )
= 
= a
y = (x - 3)² + 1 ← in vertex form
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the equation of a parabola in factored form is
y = a(x - a)(x - b)
where a, b are the zeros and a is a multiplier
here zeros are - 1 and 3 , the factors are
(x - (- 1) ) and (x - 3), that is (x + 1) and (x - 3)
y = a(x + 1)(x - 3)
to find a substitute any other point that lies on the graph into the equation.
using (0, - 3 )
- 3 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )
1 = a
y = (x + 1)(x - 3) ← in factored form
So you multiply 2 1/3times 1 1/2 and you get 3 and 1/6
Answer:
Step-by-step explanation:
Let Alex's age = x
Mark's age = y
Luke's age = a
x + y + z = 12
The possible combinations for their age are
1. 6, 3, 3
2. 3, 3, 6
3. 4,4, 4
4, 2, 2, 8
5. 8, 2, 2
6. 2, 8, 2
7. 9, 2, 1
Etc the age can keep going as long as you can find any three numbers and add them to give you 12
What terms govern the length of this side?The basic rule of the triangle.First side length must be less than the sum of the other two sides.So to find X we must take the largest side of the triangles and compare them with amounts from other sides.
5+x>12
8+x>20 and it's system
x>7
x>12
general solution is x>12
<span>The least possible integral is 13.
PS: It's may be </span>yet 12, but in this case, triangle BCD become segment.
Answer: 1
Step-by-step explanation:
Rewrite as (i^4)^6
Rewrite i^4 as 1
Rewrite i^4 as (i^2) ^2
((i^2)) ^2)6
Rewrite i^2 as -1
((-1) ^2) 6
Raise -1 to the power of 2
1^6
One to any power is 1.
